Question

Find the area of the figure in square cm correct to one place of decimal `("take"  π = 22/7)`.

Answer 1

Given:

π = `22/7`.

Rectangle of dimensions 10 cm (length) × 10 cm (height).

A semicircle attached to the right with diameter = 10 cm radius r = 5 cm.

An isosceles triangle (cut out from the left) with equal sides 6 cm and base 10 cm.

Step-wise calculation:

1. Rectangle area

= Length × Height

= 10 × 10

= 100 cm²

2. Area of the isosceles triangle (sides 6, 6, base 10):

Height (depth into the rectangle)

h = `sqrt(6^2 - (10/2)^2)` 

= `sqrt(36 - 25)`

= `sqrt(11)`

Triangle area = `1/2` × base × h

= `1/2 xx 10 × sqrt(11)`

= `5sqrt(11)`

= 16.5831 cm²

3. Area of the semicircle (radius 5 cm):

Semicircle area = `1/2 πr^2` 

= `1/2 xx 22/7 xx 5^2` 

= `11/7 xx 25` 

= `275/7`

= 39.2857 cm²

4. Total area = Rectangle – Triangle removed + Semicircle added

= `100 - 5sqrt(11) + 275/7`

= 100 – 16.58312395 + 39.28571429

= 122.70259034 cm²

Total area = 122.7 cm².